A. Skopenkov

collaborators

3 papers

math.GT2026

Embeddability of joinpowers, and minimal rank of partial matrices

A. Skopenkov, O. Styrt

A general position map $f : K \to M$ of a $k$ -dimensional simplicial complex to a $2 k$ -dimensional manifold (for $k = 1$ , of a graph to a surface) is a $Z_{2}$ -embedding if $|fÏ\…

math.GT2026

A short proof of the Patak-Tancer theorem on non-embeddability of $k$ -complexes in $2 k$ -manifolds

E. Kogan, A. Skopenkov

In 2019 P. Patak and M. Tancer obtained the following higher-dimensional generalization of the Heawood inequality on embeddings of graphs into surfaces. We present a short well-str…

math.CO2025

A quadratic estimation for the KÃ¼hnel conjecture on embeddings

S. Dzhenzher, A. Skopenkov

The classical Heawood inequality states that if the complete graph $K_{n}$ on $n$ vertices is embeddable in the sphere with $g$ handles, then $g \geq \frac{( n - 3 ) ( n - 4 )}{12}$ . A higher-…

Embeddability of joinpowers, and minimal rank of partial matrices

A short proof of the Patak-Tancer theorem on non-embeddability of k-complexes in 2k-manifolds

A quadratic estimation for the KÃ¼hnel conjecture on embeddings

A short proof of the Patak-Tancer theorem on non-embeddability of $k$ -complexes in $2 k$ -manifolds